Summary Statistics
Species tables and tree tables
## Parsed with column specification:
## cols(
## Species = col_character(),
## `Scientific Name` = col_character(),
## `Func. Group` = col_character(),
## Sightings = col_double(),
## Ingestions = col_double(),
## Removals = col_double(),
## Nibbles = col_double(),
## `Avg. Vistitation Rate` = col_double(),
## `Avg. Fruit Removal Rate` = col_double(),
## SDE = col_double(),
## Class = col_character()
## )
## [1] "Species" "Scientific Name"
## [3] "Func. Group" "Sightings"
## [5] "Ingestions" "Removals"
## [7] "Nibbles" "Avg. Vistitation Rate"
## [9] "Avg. Fruit Removal Rate" "SDE"
## [11] "Class"

## # A tibble: 2 x 4
## Height count mean sd
## <fct> <int> <dbl> <dbl>
## 1 high 25 0.301 0.387
## 2 low 45 0.0516 0.0580
## TH Tree Height visits fruit.rem.rate SDE
## 1 258_low 258 low 0.36210317 0.150000000 0.054315476
## 2 258_high 258 high 1.01686508 0.524450549 0.533295450
## 3 13_low 13 low 1.25000000 0.153005464 0.191256831
## 4 13_high 13 high 0.77380952 0.634146341 0.490708479
## 5 18_low 18 low 0.20568783 0.006410256 0.001318512
## 6 79_low 79 low 0.76315438 0.153846154 0.117408366
## 7 79_high 79 high 2.00983045 0.559900109 1.125304287
## 8 250_high 250 high 0.00000000 0.000000000 0.000000000
## 9 388_high 388 high 1.59523810 0.806991774 1.287344021
## 10 388_low 388 low 0.51785714 0.054347826 0.028144410
## 11 406_low 406 low 1.31944444 0.098039216 0.129357298
## 12 406_high 406 high 0.62500000 0.571428571 0.357142857
## 13 200_low 200 low 1.51515152 0.115942029 0.175669741
## 14 203_low 203 low 2.17532468 0.066798523 0.145308476
## 15 6_high 6 high 0.19439935 0.702077922 0.136483492
## 16 6_low 6 low 0.11842324 0.080536312 0.009537371
## 17 75_low 75 low 0.15625000 0.000000000 0.000000000
## 18 203_high 203 high 0.25595238 0.731884058 0.187327467
## 19 90_high 90 high 0.42981902 0.561310976 0.241262135
## 20 205_low 205 low 0.24122807 0.136363636 0.032894737
## 21 25_high 25 high 0.03472222 1.000000000 0.034722222
## 22 41_low 41 low 0.00000000 0.000000000 0.000000000
## 23 41_high 41 high 0.28645833 0.714285714 0.204613095
## 24 92_low 92 low 0.28905508 0.070530733 0.020387267
## 25 67_high 67 high 0.37500000 1.000000000 0.375000000
## 26 262_low 262 low 0.06410256 0.000000000 0.000000000
## 27 293_high 293 high 0.00000000 0.000000000 0.000000000
## 28 8_low 8 low 0.07575758 0.000000000 0.000000000
## 29 19_low 19 low 0.00000000 0.000000000 0.000000000
## 30 144_low 144 low 0.64406318 0.177388836 0.114249618
## 31 160_high 160 high 0.00000000 0.000000000 0.000000000
## 32 90_low 90 low 0.09572218 0.190476190 0.018232796
## 33 138_high 138 high 0.35054200 0.456794294 0.160125586
## 34 138_low 138 low 0.32778922 0.258405694 0.084702600
## 35 127_low 127 low 0.07502914 0.104761905 0.007860195
## 36 127_high 127 high 0.06944444 0.750000000 0.052083333
## 37 60_low 60 low 0.00000000 0.000000000 0.000000000
## 38 82_high 82 high 1.64368964 0.769627660 1.265029014
## 39 82_low 82 low 0.72448385 0.253885148 0.183935689
## 40 107_low 107 low 0.06578947 0.666666667 0.043859649
## 41 121_low 121 low 0.05341880 0.046875000 0.002504006
## 42 121_high 121 high 0.00000000 0.000000000 0.000000000
## 43 141_low 141 low 0.30102710 0.256465517 0.077203070
## 44 160_low 160 low 0.49533800 0.106162431 0.052586286
## 45 23_low 23 low 0.04941239 0.175000000 0.008647169
## 46 399_high 399 high 0.23103632 0.159663866 0.036888153
## 47 399_low 399 low 0.23698524 0.303921569 0.072024925
## 48 84_low 84 low 0.20834691 0.120035703 0.025009067
## 49 134_low 134 low 0.07470539 0.128205128 0.009577614
## 50 384_low 384 low 0.24621212 0.416666667 0.102588384
## 51 84_high 84 high 0.00000000 0.000000000 0.000000000
## 52 197_high 197 high 0.72916667 0.565217391 0.412137681
## 53 197_low 197 low 0.78125000 0.026666667 0.020833333
## 54 46_low 46 low 0.45454545 0.064814815 0.029461279
## 55 53_low 53 low 0.11363636 0.000000000 0.000000000
## 56 129_high 129 high 0.00000000 0.000000000 0.000000000
## 57 129_low 129 low 0.57849702 0.090425532 0.052310901
## 58 17_low 17 low 0.41666667 0.070422535 0.029342723
## 59 54_low 54 low 0.23674242 0.169706180 0.040176653
## 60 89_low 89 low 0.07352941 0.120000000 0.008823529
## 61 295_high 295 high 0.96590909 0.424640400 0.410164023
## 62 295_low 295 low 0.48413826 0.225877193 0.109355791
## 63 83_low 83 low 1.10294118 0.133858268 0.147637795
## 64 92_high 92 high 0.19943020 0.358333333 0.071462488
## 65 97_low 97 low 0.05208333 0.000000000 0.000000000
## 66 269_low 269 low 0.06410256 0.500000000 0.032051282
## 67 26_low 26 low 0.00000000 0.000000000 0.000000000
## 68 72_low 72 low 0.49242424 0.288888889 0.142255892
## 69 72_high 72 high 0.29166667 0.500000000 0.145833333
## 70 265_low 265 low 0.00000000 0.000000000 0.000000000

##
## Kruskal-Wallis rank sum test
##
## data: SDE by Height
## Kruskal-Wallis chi-squared = 8.7213, df = 1, p-value = 0.003145
## Df Sum Sq Mean Sq F value Pr(>F)
## Height 1 1.000 1.0005 18.15 6.43e-05 ***
## Residuals 68 3.748 0.0551
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Loading required package: carData
## Registered S3 methods overwritten by 'car':
## method from
## influence.merMod lme4
## cooks.distance.influence.merMod lme4
## dfbeta.influence.merMod lme4
## dfbetas.influence.merMod lme4
##
## Attaching package: 'car'
## The following object is masked from 'package:boot':
##
## logit
## The following object is masked from 'package:psych':
##
## logit
## The following object is masked from 'package:purrr':
##
## some
## The following object is masked from 'package:dplyr':
##
## recode
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 19.494 3.705e-05 ***
## 68
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Checking significance in differences of SDE
## Parsed with column specification:
## cols(
## Species = col_character(),
## `Scientific Name` = col_character(),
## `Func. Group` = col_character(),
## Sightings = col_double(),
## Ingestions = col_double(),
## Removals = col_double(),
## Nibbles = col_double(),
## `Avg. Vistitation Rate` = col_double(),
## `Avg. Fruit Removal Rate` = col_double(),
## SDE = col_double(),
## Class = col_character()
## )

## file saved to Table3.png
## file saved to SPPtable.pdf
## Note that HTML color may not be displayed on PDF properly.
## [1] "FD" "NFD"
## # A tibble: 2 x 4
## `Func. Group` count mean sd
## <fct> <int> <dbl> <dbl>
## 1 FD 7 2.14 2.05
## 2 NFD 13 0.446 0.454
## # A tibble: 20 x 11
## Species `Scientific Nam… `Func. Group` Sightings Ingestions Removals Nibbles
## <chr> <chr> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 Centra… "Dasyprocta pun… NFD 260 0 44 70
## 2 Brown … "Metachirus nud… NFD 82 2 2 4
## 3 Baudó … "Penelope orton… FD 20 2 4 2
## 4 Choco … "Ramphastos bre… FD 272 99 142 3
## 5 Chestn… "Ramphastos amb… FD 316 157 168 1
## 6 South … "Nasua nasua " NFD 458 2 0 175
## 7 Collar… "Pecari tajacu" NFD 136 4 0 0
## 8 Kinkaj… "Potos flavus" NFD 84 0 3 14
## 9 Oilbird "Steatornis car… FD 73 0 36 0
## 10 Common… "Didelphis mars… NFD 100 1 0 27
## 11 Lowlan… "Cuniculus paca" NFD 416 0 31 73
## 12 Rufous… "Odontophorus e… NFD 434 0 0 4
## 13 Rodent… "" NFD 1380 0 197 45
## 14 Rufous… "Diplomys labil… NFD 5 0 0 1
## 15 Southe… "Amazona farino… FD 10 0 7 0
## 16 Squirr… "" NFD 675 0 249 109
## 17 Toucan… "" FD 284 75 85 0
## 18 Tome's… "Proechimys sem… NFD 136 0 24 1
## 19 Long-w… "Cephalopterus … FD 269 34 96 2
## 20 Brown … "Aramides wolfi" NFD 127 0 0 7
## # … with 4 more variables: `Avg. Vistitation Rate` <dbl>, `Avg. Fruit Removal
## # Rate` <dbl>, SDE <dbl>, Class <chr>


##
## One-way analysis of means (not assuming equal variances)
##
## data: SDE and Func_group
## F = 4.641, num df = 1.0000, denom df = 6.3171, p-value = 0.07238
##
## Kruskal-Wallis rank sum test
##
## data: SDE by Func_group
## Kruskal-Wallis chi-squared = 5.3009, df = 1, p-value = 0.02131
## Df Sum Sq Mean Sq F value Pr(>F)
## Func_group 1 13.05 13.054 8.462 0.00936 **
## Residuals 18 27.77 1.543
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SDE ~ Func_group, data = spptable)
##
## $Func_group
## diff lwr upr p adj
## NFD-FD -1.693846 -2.917178 -0.4705144 0.0093621
## Df Sum Sq Mean Sq F value Pr(>F)
## Class 1 6.40 6.401 3.347 0.0839 .
## Residuals 18 34.42 1.912
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SDE ~ Class, data = spptable)
##
## $Class
## diff lwr upr p adj
## Mammal-Bird -1.137172 -2.443006 0.1686627 0.0839294
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 6.2905 0.02194 *
## 18
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 5.2885 0.03365 *
## 18
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Model Comparisons
Model 1: Original
## real.visitation ~ focalmonth..50 * Height + offset(lograte) +
## (1 + focalmonth..50 | Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.0405307
|
0.1886986
|
0.2147905
|
0.8299306
|
|
focalmonth..50
|
0.5152201
|
0.2956979
|
1.7423871
|
0.0814407
|
|
Heightlow
|
0.7238617
|
0.0437088
|
16.5610200
|
0.0000000
|
|
focalmonth..50:Heightlow
|
-0.2752461
|
0.0374950
|
-7.3408839
|
0.0000000
|
## real.visitation ~ focalmonth..450 * Height + offset(lograte) +
## (1 + focalmonth..450 | Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.2234468
|
0.3520308
|
0.6347365
|
0.5256003
|
|
focalmonth..450
|
-0.0047342
|
0.0302651
|
-0.1564254
|
0.8756977
|
|
Heightlow
|
0.4050716
|
0.0852282
|
4.7527900
|
0.0000020
|
|
focalmonth..450:Heightlow
|
0.0042980
|
0.0059529
|
0.7220041
|
0.4702920
|
## Parsed with column specification:
## cols(
## X1 = col_character(),
## `z/tau value` = col_double(),
## `±SE` = col_double(),
## `p value` = col_double()
## )

## file saved to TableGLMM2.pdf
Model 2: Trees without any visits from Dispersers are removed
## real.visitation ~ focalmonth..50 * Height + offset(lograte) +
## (1 + focalmonth..50 | Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.0415496
|
0.1880433
|
0.2209575
|
0.8251255
|
|
focalmonth..50
|
0.5152245
|
0.2960341
|
1.7404230
|
0.0817848
|
|
Heightlow
|
0.7235774
|
0.0436765
|
16.5667539
|
0.0000000
|
|
focalmonth..50:Heightlow
|
-0.2750984
|
0.0374846
|
-7.3389674
|
0.0000000
|
Results are qualitatively similar.
Model 3: Original amount of trees, but fruiting neighborhood is now binary
## real.visitation ~ bin50 * Height + offset(lograte) + (1 + bin50 |
## Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.0439227
|
0.1998483
|
0.219780
|
0.8260425
|
|
bin501
|
0.5713877
|
0.3322725
|
1.719636
|
0.0854987
|
|
Heightlow
|
0.6624992
|
0.0483892
|
13.691042
|
0.0000000
|
|
bin501:Heightlow
|
-0.3084512
|
0.0692597
|
-4.453547
|
0.0000084
|
Again, binarizing is qualitatively similar.
Model 4: Original amount of trees, but fruiting neighborhood categorized into 0,1,2,3+
## real.visitation ~ bin50 * Height + offset(lograte) + (1 | Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.1688387
|
0.1767227
|
0.9553876
|
0.3393817
|
|
bin50(1)
|
0.1033138
|
0.0840268
|
1.2295336
|
0.2188718
|
|
bin50(2)
|
0.0176622
|
0.1071663
|
0.1648108
|
0.8690929
|
|
bin50(3)
|
-0.4130312
|
0.1485860
|
-2.7797440
|
0.0054402
|
|
Heightlow
|
0.6869025
|
0.0479722
|
14.3187591
|
0.0000000
|
|
bin50(1):Heightlow
|
-0.2540545
|
0.0754133
|
-3.3688264
|
0.0007549
|
|
bin50(2):Heightlow
|
-0.8947907
|
0.1114449
|
-8.0289979
|
0.0000000
|
|
bin50(3):Heightlow
|
-0.2842984
|
0.1605031
|
-1.7712948
|
0.0765117
|
Model 5: Original data but tree with outlier in visitation in high cameras removed
## real.visitation ~ focalmonth..50 * Height + offset(lograte) +
## (1 + focalmonth..50 | Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.0650785
|
0.1908849
|
0.3409307
|
0.7331558
|
|
focalmonth..50
|
0.3663191
|
0.3096886
|
1.1828626
|
0.2368636
|
|
Heightlow
|
0.6933769
|
0.0439534
|
15.7752735
|
0.0000000
|
|
focalmonth..50:Heightlow
|
-0.0700859
|
0.0400875
|
-1.7483212
|
0.0804084
|
Focalmonth..50 and the interaction term are no longer significant.
Model 6: Trees without any visits from Dispersers are removed AND outlier in visitation in high cameras removed
## real.visitation ~ focalmonth..50 * Height + offset(lograte) +
## (1 + focalmonth..50 | Tree)
|
|
Estimate
|
Std. Error
|
z value
|
Pr(>|z|)
|
|
(Intercept)
|
0.0657147
|
0.1905568
|
0.3448563
|
0.7302024
|
|
focalmonth..50
|
0.3664713
|
0.3096947
|
1.1833307
|
0.2366781
|
|
Heightlow
|
0.6931354
|
0.0439257
|
15.7797227
|
0.0000000
|
|
focalmonth..50:Heightlow
|
-0.0699615
|
0.0400800
|
-1.7455466
|
0.0808898
|
Results are qualitatively similar again when trees with 0 disperser visitation is removed
Correlation between Fruiting neighborhood (FN) at 50m and for FN at whole study plot




##
## Shapiro-Wilk normality test
##
## data: dummy$fn1400
## W = 0.93961, p-value = 4.615e-06
##
## Shapiro-Wilk normality test
##
## data: dummy$FN50
## W = 0.69195, p-value < 2.2e-16
Correlation between fruiting neighborhood at 50 m and entire plot.
|
statistic
|
p.value
|
kendall_score
|
denominator
|
var_kendall_score
|
|
0.1360697
|
0.0378435
|
1118
|
8216.378
|
289349.8
|

Model 1: total rate ~ FN50 + FNTotal + Camera height
Model 2: Fd rate ~ FN50 + FNTotal + Camera height
Model 3.5 Models
## Family: poisson ( log )
## Formula:
## total.V ~ FN50 * fn1400 + Height + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 1966.5 1990.7 -975.3 1950.5 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 0.778 0.882
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -4.924e-01 1.867e-01 -2.638 0.00834 **
## FN50 -1.662e-01 1.570e-01 -1.059 0.28964
## fn1400 3.990e-02 7.766e-03 5.138 2.78e-07 ***
## Heightlow -5.404e-01 5.240e-02 -10.313 < 2e-16 ***
## FN50:fn1400 5.275e-05 7.173e-03 0.007 0.99413
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0242 0.2246 -4.560 5.12e-06 ***
## FN50 -0.1824 0.2141 -0.852 0.394
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Family: poisson ( log )
## Formula: FD.V ~ FN50 * fn1400 + Height + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 967.2 991.3 -475.6 951.2 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 1.55 1.245
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.80919 0.28804 -2.809 0.00497 **
## FN50 -1.02918 0.26078 -3.947 7.93e-05 ***
## fn1400 0.05025 0.01291 3.894 9.87e-05 ***
## Heightlow -1.97516 0.22285 -8.863 < 2e-16 ***
## FN50:fn1400 0.03195 0.01158 2.760 0.00579 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.1271 0.2412 0.527 0.598
## FN50 0.2714 0.2235 1.214 0.225

## Family: poisson ( log )
## Formula: TD.V ~ FN50 * fn1400 + Height + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 982.3 1006.5 -483.2 966.3 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 0.7233 0.8505
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.75049 0.30000 -2.502 0.0124 *
## FN50 0.61528 0.30310 2.030 0.0424 *
## fn1400 0.01215 0.01217 0.998 0.3181
## Heightlow 0.19858 0.11980 1.658 0.0974 .
## FN50:fn1400 -0.03165 0.01368 -2.313 0.0207 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.06295 0.20202 -0.312 0.755
## FN50 -0.21965 0.17130 -1.282 0.200
|
Â
|
Visitation rate with random intercept
|
Visitation rate with random intercept AND SLOPE
|
Flying visitation rate with random intercept
|
|
Predictors
|
Incidence Rate Ratios
|
CI
|
p
|
Incidence Rate Ratios
|
CI
|
p
|
Incidence Rate Ratios
|
CI
|
p
|
|
(Intercept)
|
0.61
|
0.42 – 0.88
|
0.008
|
0.45
|
0.25 – 0.78
|
0.005
|
0.47
|
0.26 – 0.85
|
0.012
|
|
FN50
|
0.85
|
0.62 – 1.15
|
0.290
|
0.36
|
0.21 – 0.60
|
<0.001
|
1.85
|
1.02 – 3.35
|
0.042
|
|
fn1400
|
1.04
|
1.02 – 1.06
|
<0.001
|
1.05
|
1.03 – 1.08
|
<0.001
|
1.01
|
0.99 – 1.04
|
0.318
|
|
Height [low]
|
0.58
|
0.53 – 0.65
|
<0.001
|
0.14
|
0.09 – 0.21
|
<0.001
|
1.22
|
0.96 – 1.54
|
0.097
|
|
FN50 * fn1400
|
1.00
|
0.99 – 1.01
|
0.994
|
1.03
|
1.01 – 1.06
|
0.006
|
0.97
|
0.94 – 1.00
|
0.021
|
|
Zero-Inflated Model
|
|
(Intercept)
|
0.36
|
0.23 – 0.56
|
<0.001
|
1.14
|
0.71 – 1.82
|
0.598
|
0.94
|
0.63 – 1.40
|
0.755
|
|
FN50
|
0.83
|
0.55 – 1.27
|
0.394
|
1.31
|
0.85 – 2.03
|
0.225
|
0.80
|
0.57 – 1.12
|
0.200
|
|
Random Effects
|
|
σ2
|
0.71
|
1.70
|
0.55
|
|
τ00
|
0.78 Tree
|
1.55 Tree
|
0.72 Tree
|
|
ICC
|
0.52
|
0.48
|
0.57
|
|
N
|
47 Tree
|
47 Tree
|
47 Tree
|
|
Observations
|
151
|
151
|
151
|
|
Marginal R2 / Conditional R2
|
0.094 / 0.567
|
0.287 / 0.628
|
0.025 / 0.576
|
|
AIC
|
1966.533
|
967.186
|
982.329
|
|
|
Estimate
|
Estimate
|
Estimate
|
|
(Intercept)
|
-0.4924035
|
-0.8091924
|
-0.7504906
|
|
FN50
|
-0.1662483
|
-1.0291770
|
0.6152846
|
|
fn1400
|
0.0398962
|
0.0502546
|
0.0121530
|
|
Heightlow
|
-0.5404348
|
-1.9751555
|
0.1985775
|
|
FN50:fn1400
|
0.0000527
|
0.0319515
|
-0.0316486
|
Model 4: All models including crop size but no interaction terms
## Family: poisson ( log )
## Formula:
## total.V ~ FN50 + Height + fn1400 + cropsize + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 1901.7 1934.9 -939.8 1879.7 140
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 0.7214 0.8494
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.563966 0.236021 -2.389 0.01687 *
## FN50 -0.120211 0.043809 -2.744 0.00607 **
## Heightlow -0.595176 0.054561 -10.908 < 2e-16 ***
## fn1400 0.036728 0.008522 4.310 1.63e-05 ***
## cropsize.L 0.166032 0.254977 0.651 0.51494
## cropsize.Q -0.442950 0.222020 -1.995 0.04603 *
## cropsize.C 0.014846 0.183665 0.081 0.93557
## cropsize^4 0.512372 0.111204 4.608 4.08e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0026 0.2250 -4.455 8.38e-06 ***
## FN50 -0.1581 0.2043 -0.774 0.439
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: dummy
## Models:
## m2: total.V ~ FN50 + Height + fn1400 + (1 | Tree) + offset(lograte), zi=~FN50, disp=~1
## model.1RIcrop: total.V ~ FN50 + Height + fn1400 + cropsize + offset(lograte) + , zi=~FN50, disp=~1
## model.1RIcrop: (1 | Tree), zi=~FN50, disp=~1
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m2 7 1964.5 1985.7 -975.27 1950.5
## model.1RIcrop 11 1901.7 1934.9 -939.85 1879.7 70.837 4 1.511e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # R2 for Mixed Models
##
## Conditional R2: 0.562
## Marginal R2: 0.127
## FN50 Height fn1400 cropsize emmean SE df lower.CL upper.CL
## 0.662 high 17.3 a 2.17 0.430 140 1.322 3.02
## 0.662 low 17.3 a 1.58 0.426 140 0.735 2.42
## 0.662 high 17.3 b 2.29 0.240 140 1.814 2.76
## 0.662 low 17.3 b 1.69 0.244 140 1.209 2.18
## 0.662 high 17.3 c 3.06 0.173 140 2.720 3.40
## 0.662 low 17.3 c 2.47 0.169 140 2.132 2.80
## 0.662 high 17.3 d 2.37 0.172 140 2.034 2.71
## 0.662 low 17.3 d 1.78 0.171 140 1.440 2.12
## 0.662 high 17.3 e 2.39 0.179 140 2.038 2.74
## 0.662 low 17.3 e 1.80 0.181 140 1.438 2.16
##
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95

## Family: poisson ( log )
## Formula: FD.V ~ FN50 + Height + fn1400 + cropsize + offset(lograte) +
## (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## NA NA NA NA 140
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 2.005 1.416
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.142008 0.100966 -11.31 < 2e-16 ***
## FN50 -0.351001 0.078046 -4.50 6.88e-06 ***
## Heightlow -2.389815 0.194816 -12.27 < 2e-16 ***
## fn1400 0.027412 0.003297 8.31 < 2e-16 ***
## cropsize.L 3.122236 0.264788 11.79 < 2e-16 ***
## cropsize.Q -2.426704 0.030621 -79.25 < 2e-16 ***
## cropsize.C 2.091143 0.143001 14.62 < 2e-16 ***
## cropsize^4 -0.539855 0.163815 -3.30 0.000982 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.1757 0.2565 -0.685 0.493
## FN50 0.4473 0.1063 4.206 2.6e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Not enough model terms in the zero_inflated part of the model to check for multicollinearity.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

## Data: dummy
## Models:
## model.2crop: FD.V ~ FN50 + Height + fn1400 + cropsize + offset(lograte) + , zi=~FN50, disp=~1
## model.2crop: (1 | Tree), zi=~FN50, disp=~1
## m2: FD.V ~ FN50 + Height + fn1400 + cropsize + (1 | Tree) + offset(lograte), zi=~FN50, disp=~1
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## model.2crop 11
## m2 11 0

## Data: dummy
## Models:
## model.3crop: TD.V ~ FN50 + Height + fn1400 + cropsize + offset(lograte) + , zi=~FN50, disp=~1
## model.3crop: (1 | Tree), zi=~FN50, disp=~1
## m2: TD.V ~ FN50 + Height + fn1400 + cropsize + (1 | Tree) + offset(lograte), zi=~FN50, disp=~1
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## model.3crop 11 930.3 963.49 -454.15 908.3
## m2 11 930.3 963.49 -454.15 908.3 0 0 1
|
Â
|
total.V
|
FD.V
|
TD.V
|
|
Predictors
|
Incidence Rate Ratios
|
CI
|
p
|
Incidence Rate Ratios
|
CI
|
p
|
Incidence Rate Ratios
|
CI
|
p
|
|
(Intercept)
|
0.57
|
0.36 – 0.90
|
0.017
|
0.32
|
0.26 – 0.39
|
<0.001
|
0.30
|
0.15 – 0.62
|
0.001
|
|
FN50
|
0.89
|
0.81 – 0.97
|
0.006
|
0.70
|
0.60 – 0.82
|
<0.001
|
0.88
|
0.78 – 0.98
|
0.022
|
|
Height [low]
|
0.55
|
0.50 – 0.61
|
<0.001
|
0.09
|
0.06 – 0.13
|
<0.001
|
1.40
|
1.09 – 1.80
|
0.009
|
|
fn1400
|
1.04
|
1.02 – 1.05
|
<0.001
|
1.03
|
1.02 – 1.03
|
<0.001
|
1.00
|
0.98 – 1.03
|
0.792
|
|
cropsize.L
|
1.18
|
0.72 – 1.95
|
0.515
|
22.70
|
13.51 – 38.14
|
<0.001
|
2.65
|
1.35 – 5.20
|
0.005
|
|
cropsize.Q
|
0.64
|
0.42 – 0.99
|
0.046
|
0.09
|
0.08 – 0.09
|
<0.001
|
0.78
|
0.43 – 1.41
|
0.403
|
|
cropsize.C
|
1.01
|
0.71 – 1.45
|
0.936
|
8.09
|
6.12 – 10.71
|
<0.001
|
0.52
|
0.19 – 1.40
|
0.194
|
|
cropsize^4
|
1.67
|
1.34 – 2.08
|
<0.001
|
0.58
|
0.42 – 0.80
|
0.001
|
3.50
|
1.72 – 7.12
|
0.001
|
|
Zero-Inflated Model
|
|
(Intercept)
|
0.37
|
0.24 – 0.57
|
<0.001
|
0.84
|
0.51 – 1.39
|
0.493
|
0.87
|
0.52 – 1.47
|
0.611
|
|
FN50
|
0.85
|
0.57 – 1.27
|
0.439
|
1.56
|
1.27 – 1.93
|
<0.001
|
0.82
|
0.56 – 1.18
|
0.280
|
|
Random Effects
|
|
σ2
|
0.73
|
2.05
|
0.51
|
|
τ00
|
0.72 Tree
|
2.00 Tree
|
0.63 Tree
|
|
ICC
|
0.50
|
0.49
|
0.55
|
|
N
|
47 Tree
|
47 Tree
|
47 Tree
|
|
Observations
|
151
|
151
|
151
|
|
Marginal R2 / Conditional R2
|
0.127 / 0.562
|
0.321 / 0.656
|
0.197 / 0.638
|
Model 5: cropsize again but binarized with low being below 500
## Family: poisson ( log )
## Formula:
## total.V ~ FN50 + Height + fn1400 + csizeb + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 1920.2 1944.3 -952.1 1904.2 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 0.7294 0.854
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.596084 0.207320 -2.875 0.00404 **
## FN50 -0.120066 0.044043 -2.726 0.00641 **
## Heightlow -0.569945 0.053448 -10.664 < 2e-16 ***
## fn1400 0.035523 0.007259 4.893 9.91e-07 ***
## csizebLow 0.508652 0.073704 6.901 5.15e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0017 0.2234 -4.484 7.32e-06 ***
## FN50 -0.1551 0.2037 -0.761 0.447
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Family: poisson ( log )
## Formula:
## FD.V ~ FN50 + Height + fn1400 + csizeb + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 972.6 996.7 -478.3 956.6 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 1.563 1.25
## Number of obs: 151, groups: Tree, 47
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.07453 0.28910 -3.717 0.000202 ***
## FN50 -0.32242 0.08240 -3.913 9.12e-05 ***
## Heightlow -2.24234 0.26167 -8.569 < 2e-16 ***
## fn1400 0.06250 0.01169 5.344 9.08e-08 ***
## csizebLow 0.19925 0.12580 1.584 0.113234
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.06932 0.25576 0.271 0.786
## FN50 0.28032 0.22452 1.248 0.212
## Family: tweedie ( log )
## Formula:
## TD.V ~ FN50 + Height + fn1400 + csizeb + offset(lograte) + (1 | Tree)
## Zero inflation: ~FN50
## Data: dummy
##
## AIC BIC logLik deviance df.resid
## 748.0 778.2 -364.0 728.0 141
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## Tree (Intercept) 0.4007 0.633
## Number of obs: 151, groups: Tree, 47
##
## Overdispersion parameter for tweedie family (): 4.89
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.22212 0.48325 -6.668 2.60e-11 ***
## FN50 -0.03436 0.12926 -0.266 0.7904
## Heightlow 1.76597 0.27139 6.507 7.66e-11 ***
## fn1400 0.04854 0.02040 2.379 0.0174 *
## csizebLow 0.47916 0.25973 1.845 0.0651 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -19.320 5643.465 -0.003 0.997
## FN50 -2.112 14674.518 0.000 1.000
